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Nonlinear evolution equations are the mathematical models for time-dependent processes in science andengineering. We focus on models enriched by, e.g., nonlocality in time or space as well as on non-standardassumptions as, e.g., non-monotone growth. We study existence of generalized solutions via convergenceof suitable approximation schemes. Applications arise in soft matter and dynamics of complex fluids.We aim to study models for smectic phases as well as nonlocal models of liquid crystals and to applythe new concept of relative energy.